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21320013ProceedingsoftheCSEEVol.21No.3Mar.2001n2001Chin.Soc.forElec.Eng.:025828013(2001)0320006206PI1,2,2(1.,130012;2.,110006)PISLIDINGMODELOADFREQUENCYCONTROLOFMULTI2AREAPOWERSYSTEMSMENGXiang2ping1,XUEChang2fei2,ZHANGHua2guang2(1.ChangchunInstituteofTechnology,Changchun,130012,China;2.NortheasternUniversity,Shenyang,110006,China)ABSTRACT:AsyntheticPIslidingmodecontrolmethodusedforloadfrequencycontrolofmultiareapowersystemshasbeenproposed,themethodhastheadvantagesofPIandslidingmodecontrol,slidingmodesuperfacewithintegralitemmakethesys2temcanreachonslidingmodefrominitialtime.Afterreachingonslidingmode,systemiscontrolledbyPIcontrolbasedonA2CEN.Whenconsideringgenerationrateconstraint(GRC)anddeadband,theproposedsyntheticcontrolmethodcanmakesys2temtohavegoodperformance,andcanovercomethedisadvan2tagesofeachcontrolmethod.Resultsofsimulationshowthattheproposedmethodissimple,effective,andtoensurethatthewholesystemsareasymptoticstable.KEYWORDS:loadfrequencycontrol;PIcontrol;slidingmodecontrol;robustness;decentralisedcontrol;powersystem.:PI,,,,,,,:;PI;;;;:TP273;TM732:A1,:(69404003);(96014518)[1],PIPtiefACE,IKothari[2]ACENLFC(loadfre2quencycontrol),ACENPIPI,I,GRC(generationrateconstraint),,[3]Tp20%,,GRC,,ACENPI,PI,,,,,,,,,GRC,2,n1,Tgi;Tti;Tpi;Tri;Ri;i;Kri;Kpi;Pgi;Xei;Pci;ui;Pdi;fi;Ptiei;Pri;Tijij2.11Fig.1DynamicmodeldiagramofelectricpowersystemÛX=AX+Bu+FPdX(0)=0(1)X=[X1,X2,,Xn]T,u=[u1,u2,,un]T,Pd=[Pd1,Pd2,,Pdn]T;Xi,ui,Pdii,Xi=[fi,Pgi,Pri,Xei,Ptiei,ACEidt,ACENidt,ACENi]TA=A11A12A1nA21A22A2nAn1An2AnnAiiAijB=[B1,B2,Bn]TBi=[00KriTgi1Tgi0000]TF=[F1,F2,Fn]TFi=[-KpiTpi000000-iKpiTpi]T,i=1,2,n2.2LFC,2:LFC;LFC,,0.1/min,,[4],2s,F(x,Ûx)=0.8x-0.2Ûxx=u-1Rf,0.05%73:PI3PI,1,,,n[5]3.1i,:ÛXi=AiiXi+Biui+FiPdi+6nj=1jiAijXj(2)Xjj(2),ÛXi=(Aii+Aii)Xi+(Bi+Bi)ui+(Fi+Fi)Pdi+6nj=1jiAijXj(3)Aii,Bi,FiKpiKriTpiTriTtiTgiPdi(2)ÛXi=AiiXi+Bi(ui+fi(X,t))(4)fi(X,t)=B+iAiiXi+B+iBiui+B+i(Fi+Fi)Pdi+B+i6nj=1jiAijXj,B+i=(BTiBi)-1BTi(4),ABi,[6]:Si=Ci[Xi-t0(Aii-BiKi)Xi()d]=0(5)Ci;Ki(5),(4)(5),Si=ÛSi(t)=0(4)(6):ÛXi=(Aii-BiKi)Xi(6)(5)S=0S=0,CiKi1:Ki=[000000kiIkiP],ACENPI,,ui=-kiPACENi-kiIACENidt,PI,PI,PtiefACEI2:K,K,,LFC,GRC,,PI,(5),,:Si0,t0,Wi=t0(Aii-BiKi)Xi()dÛWi=(Aii-BiKi)XiXi(0)=0,Wi(0)=Xi(0)=0,,Ci=BTi,(5)Si=BTi(Xi-Wi)(7),Si(0)=0,,3.2(7),[7]:ui=ueqi+usi(8)ueqi,;usi,,Si=0,ueqi=-KiXi=-kipACENi-kiIACENidt,ueqi,,PIusi,Si=0,821usi=-hisng(Si)sng(Si);hi,|fi(X,t)|hi(9)SiÛSi=SiBTi(ÛXi-ÛWi)=Si{BTiAiiXi+Bi(ui+fi(X,t))-BTi(Aii-BiKi)Xi}=Si{BTi(AiiXi+Bi(-KiXi-hisgn(Si)+fi(X,t)))-BTi(Aii-BiKi)Xi}=Si{-BTiBihisgn(Si)+BTiBifi(X,t)}-BTiBihi|Si|+BTiBi|Si|fi(X,t)|0,(8)SiÛSi0(8),ueqi,ACENiPI;,usiS=0,3:,,3.31(4),(9),(8),ueqi=-KiXi,usi=-hisgn(Si),(i=1,2,,n),Ci=BTi,S=[S1S2SN]T,X(t)V(X,t)=12STS,ÛV=12ÛSTS+12STÛS=STÛS=6ni=1SiÛSi0,|fi(X,t)|hi,4252,:f=60Hz;Tpi=20s;Tgi=0.08s;Tri=10s;i=0.035;Tti=0.3s;Kri=0.5;Ri=2.4;Kpi=120Hz/pu;2Tij=0.545;i=0.42521Fig.2Dynamicresponsesofsysteminarea193:PI32Fig.3Dynamicresponseofsysteminarea24usFig.4Responseofcontroluandslidingmodesvstimet5IFig.5CurvesoftimeerrorandinadvertentinterchargeI:kip=0.15,kiI=0.02,GRC,GRC0.1min,:ÛPgi=0.0017MW/s,,PI:GRC,2;,Tp+20%GRC,,3;4s,,;5,ACENPII,ACEPI0121I,kiIkiP.5PI,GRC,,Ci=BTi,PI,,;,,,:[1].[M].:,1996.[2]KothariML,NandaJ,KoathariDP,etal.Discrete2modeauto2maticgenerationcontrolofatwo2areareheatthermalsystemwithnewareacontrolerror[J].IEEETransonPowerSystems,1989,10(5):7302738.[3]Al2hamouzAZ,AbdelMagidYL.Variablestructureloadfre2quencycontrollersformultiareainterconnectedpowersystems[J].Int.J.ElectricPowerEnergySystem,1993,15(4):2932300.[4]ChangCS,FuWH,WenFS.Loadfrequencycontrolusingge2neticalgorithmbasedfuzzygainschedulingofPIcontrollers[J].ElectricMachinesandPowerSystems,1998,26(2):39252.[5]LimKY,WangK,ZhouR.Robustdecentralisedload2frequencycontrolofmulti2areapowersystems[J].IEEProc.GenerTransm.Distrib.,1996,143(5):3772386.[6]ShyuKK,ShiehHJ.Anewswitchingsurfacesliding2modespeedcontrollerforinductionmotordrivesystems[J].IEEETranson,PE,1996,11(1):6602667.[7]DrakunovSV,UtkinVI.Slidingmodecontrolindynamicsys2tems[J].Int.J.Control,1992,55(4):102921037.Aij=00000000000000000000000000000000-2Tij00000000000000000000000-2Tij0000000Aii=-1TpiKpiTpi00-KpiTpi0000-1Tti1Tti00000-KriRiTgi0-1Tri(1Tri-KriTgi)0000-1RiTgi00-1Tgi000026Nj=1jiTij0000000i0001000i0001i00(ii-iTpi+26Nj=1jiTij)iKpiTpi00i-iKpiTpi000:2000209229;:2001201221:(19612),,,,,;(19742),,,,;(19592),,,,,()2000111999,1372,280,217;0.432,148,36,()113:PI